Our customer Cheryl asked this question a few months ago on forum.yogurtathome.com
Please have a look at the animation below
The animation shows that the most important factor is the protein component.
The protein in the milk is called ''casein'' and is the main reason for allergy. The whole milk contains about 3.4g/100 ml. milk
The vegan milk with high protein contents is the Soy milk. The protein in the soy milk is different and plant derived, so it is not casein. The soy milk is protein rich, and very close to the dairy milk. So it is the best medium for a vegan substitute for yogurt. The texture is almost similar to the dairy milk yogurt and very important, can be re-cultured like dairy yogurt. The protein content of the soy milk is about 3.2gr/100.
Coconut milk is protein rich if it's blended with the shreds and made at home. Protein contents = 2.3g/100ml
The texture is creamy, not suitable for re-cultivations.
Unlike almonds which are protein rich, the Almond milk contains a very small amount of protein or about 1g/100ml. However, this varies from brand to brand, but the protein amount is not much different>More about Almond Milk nutrition
The same is valid for rice milk and oats milk.
Check out the whole discussion at https://forum.yogurtathome.com/t/whats-the-trick-to-thickening/39